# Dark matter and the gravitational constant

I am not a real physicist, so please bear with me if my question sounds stupid to all experts around here. What I have learned about the dark matter is, that objects behave as if there was more mass than actually visible. So, there's a discrepancy between the "measured" mass and the observed movement.

As an alternative to assume dark matter being responsible for this observation, one cold also postulate that the gravitational constant G might be different in other locations in the universe or around big masses, or may be dependent on other factors like the mass itself or some unknown mechanism.

So, why does nobody take this into consideration? Does G have to be constant in the universe? Would there be side-effects that make this assumption impossible? Is there any prove or evidence that G is constant? Why do we assume that? Would a different value for G or a non-constant G be able to produce effects similar to those we see? I guess, that I am neither the first one with this idea nor that this question is unanswered yet. It's just I didn't find the answer and don't know where to look for it or whom to ask. So, if anyone of you guys could briefly tell me why this idea won't work.

General Relativity a has a constant $$G$$ that represents the the strength of gravity and it can't change, with time or place, in standard General Relativity. However there are other theories such as Brans-Dicke theory, mentioned for example in the answer to this question reduction in G

The best evidence that $$G$$ is approximately constant with time comes from Lunar Laser Ranging that restricts any change with time to a very small amount.

So a formula such as $$G=\frac{Rc^2}{M}$$ from the Large Number Hypothesis, appears to be ruled out, unless it's assumed that $$R$$, the radius of the visible universe, isn't changing - i.e the universe is static, ($$M$$ is the mass of the universe). That assumption would mean very big changes for standard cosmology and most cosmologists won't entertain the idea.

Any changes in $$G$$ with position could be checked by Satellite Laser Ranging, and there are possible annual changes of order $$10^{-10}G$$ cyclic changes in G . However these variations, if they exist, would not be enough to explain the Dark Matter phenomenon, so it looks as though Dark Matter is necessary.

You might also want to look into MOND, 'Modified Newtonian Dynamics', it has a variable $$G$$

• It is only meaningful to talk about dimensionless combinations of physical constants "changing". Aug 16, 2021 at 22:26
• I don't get that. Doesn't every constant have a dimension?
– TomS
Aug 17, 2021 at 1:19